While you are likely familiar with the word “force” and have heard it used in everyday conversations (“I had no choice – he forced me to do it!”), do you know the physics definition of force?
In this article you will learn not only what a force really is, but where the idea came from and how it is used in physics.
To get in the right physics mindset for understanding forces, recall what you know about motion. You can describe an object’s position (location in space), and you can describe how that position changes in time; the rate of change of position per unit time is the velocity. You can also describe how that velocity changes – the rate of change of velocity per unit time is called acceleration.
These physical quantities – position, velocity and acceleration – are all vector quantities, meaning they have magnitude and direction associated with them.
If an object is at rest, such as a rock sitting on a sidewalk, you are likely fairly confident that it will stay there until something makes it move. Either someone walking along the sidewalk kicks it, or perhaps the rock is light enough to be pushed by a strong wind. When this occurs, its motion changes. The physical quantity that causes this change, as we will learn, is a force.
You probably also have some sense that certain objects are more difficult to move than others. Imagine a small pebble compared to a heavy boulder. You would need to kick the boulder a lot harder in order to make it move. Similarly, if two objects – a light one and a heavy one – were already moving, it’s much more difficult to make the heavier one stop.
This resistance of an object to any changes in its motion is called its inertia. How much force is required to enact a certain change will relate to mass, which is a measure of inertia.
Formalizing Forces: From Aristotle to Galileo and Newton
The idea of a force has been around for a long time, but it wasn’t well understood in a large part because of misinterpretations of friction.
Aristotle proposed that all objects have a natural state that they want to rest in and that they will do so unless a force acts. He used this notion to explain why objects fall to the earth, or slow to a stop after being pushed.
Galileo, however, refuted this idea and explained the existence of a stopping force called friction. He determined that objects would keep moving in straight-line paths if there was no friction to slow them down.
Sir Isaac Newton gave a larger formalization to Galileo’s observations with his famous three laws of motion. He was able to describe what forces do, how they act and even ascribe numbers with units to the concept.
Newton's Laws of Motion
Newton’s first law of motion – sometimes called the law of inertia – states that an object at rest remains in a state of rest unless an unbalanced force acts on it. This part is pretty intuitive when you think back to kicking the rock on the sidewalk. Furthermore, this law states that any object undergoing constant velocity motion (motion at a constant speed in a straight-line path) will continue to do so unless acted upon by a net external force.
That second part of the first law is less intuitive because in our everyday interactions, objects don’t tend to keep moving forever. But that’s because they are acted upon by a resistive force called friction.
Newton’s second law of motion states that the net force on an object (which is the vector sum of all forces acting) is equal to the product of the object’s mass and acceleration. In other words: Fnet = ma.
Newton's second law of motion was able to explain why it is that you have to push harder on heavy objects than you do on lighter objects to get them to change their motion. It also formally related force to the physical quantity of acceleration, which is the change in the object’s motion.
Newton's third law of motion further explained how forces come in pairs. It states that if object A applies force to object B, then object B applies force to object A that is equal in magnitude and in the opposite direction of the force on object B.
Newton’s third law explains why guns recoil when they are shot and why, if you stand on a skateboard and push against a wall, you end up rolling backwards.
Definition of Force
A force can be thought of as a push or a pull. If only a single force acts on an object, that single force will cause the object’s motion to change in inverse proportion to its mass.
Force is a vector quantity, meaning that it has magnitude and direction. The direction of a net force is always the same as the direction of the acceleration or change of motion (which may be opposite the direction of motion in such situations where an object is slowing down.)
The SI unit of force is the newton where 1 N = 1 kgm/s2. The CGS unit is the dyne where 1 dyne = 1gcm/s2.
Examples of Forces
You already know that you can exert a force on an object yourself by pushing it or pulling it. This is referred to as a contact force because it requires contact. But there are many other types of forces as well.
A list of some common forces you encounter when studying physics include the following:
- Gravitational force: The force of gravity on an object can be observed during free-fall motion, in which an object accelerates toward the ground. But the gravitational force is also what keeps planets in orbit, and what keeps you from flying off into space.
- Normal force: This is a support force that acts perpendicularly to a surface and is what prevents objects from falling through the floor or a table top.
- Electromagnetic force: This refers collectively to magnetic forces and electrostatic forces. These types of forces are the result of charge or moving charge. It is the reason electrons repel each other and magnets stick together.
- Frictional forces: The force of friction is a force that opposes the motion of an object. It is the reason it’s more difficult to slide a book across the table than it is to slide a book across a sheet of ice. The force of friction varies depending on the surfaces that are in contact with each other.
- Air resistance: This force is similar to friction. It results from the air itself opposing the motion of objects falling through it. If an object falls for long enough, the force of air resistance will cause it to achieve its terminal velocity.
- Tension force: This is a type of force that is transferred along a string, wire or anything similar.
- Other fundamental forces: There are four fundamental forces of nature. Two are gravity and electromagnetism, which were already listed, and the other two are the weak nuclear force and strong nuclear force. These last two typically only affect things on a subatomic scale, which is why you may have never heard of them.
Net Force and Free Body Diagrams
Newton’s second law made mention of a net force. The net force on an object is the vector sum of all forces acting on an object.
For example, you can have two people pushing on a block in opposite directions with equal forces. But the net force ends up being 0, which means the block does not move because those two forces cancel each other out.
Free body diagrams are sketches you can draw indicating the magnitude and direction of each force vector on an object with an arrow of proportional length pointing in the direction of the force. When solving physics problems involving forces, you will likely sketch a lot of these diagrams because it helps visualize what forces are acting and makes it more clear how to add the forces together to get the net force.
If there is no net force on an object, this means, via Newton’s second law, that the acceleration of the object is 0. In other words, the object must have a constant velocity.
Note that constant velocity is not the same as 0 velocity. An object moving at a constant 2 m/s for example, necessarily has no net force acting on it.
You may have heard of a force called the centripetal force. This was not listed with the other forces in the previous section because it is actually a type of net force. It is the net force in the radial direction for any object undergoing circular motion.
Circular motion, even at a constant speed, is not constant velocity motion because it does not maintain a straight-line path. Some combination of forces must act to cause circular motion. The centripetal force is the radial net force that causes this type of motion.
Do not confuse centripetal force with centrifugal force. The latter is actually considered a pseudo-force. It is the force that seems to act on an object undergoing circular motion. For example, when you are in a car that turns a corner, you may feel like you are being pressed against the side of the car, but what is actually happening is that a force is pulling you into a curved path.
Forces and Fields
Certain forces seem to act mysteriously without contact. One example you are familiar with is the gravitational force. When an object is dropped, the earth pulls that object toward it without even touching it.
One mathematical tool that physicists developed to describe this phenomenon is the notion of a field. (Yes, a “force field” but not the kind that protects you from photon torpedoes!)
A gravitational field is the assignment, to each point in space, a vector that indicates the relative magnitude and direction of the gravitational force at that location independent of what object may experience a force at that location. The value of the gravitational field at any given point would simply be the gravitational force that would be felt by a mass m at that location, but divided by m.
This notion of a force field allows for an explanation of these “mysterious” forces that seem to act without touching anything, by describing the force as resulting from an object interacting with the field.
Just like gravitational fields, you can also have an electric field or a magnetic field that describe the relative force per unit charge or (force per unit magnetic moment) that an object would feel in any particular location.